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Influence of Inhomogeneity of the Foundation on the Stress-Strain State of a Free-Lying Beam
https://orcid.org/http://orcid.org/0000-0002-7191-1237
https://orcid.org/http://orcid.org/0000-0002-1032-5373
https://orcid.org/http://orcid.org/0000-0002-0998-4726
https://orcid.org/http://orcid.org/0000-0002-0251-9258
The stress-strain state of beams freely lying on an inhomogeneous elastic Winkler foundation is investigated. It is accepted that the value of the base bed coefficient has a symmetrical character of change relative to the middle of the beam, and within its limits is described by a quadratic law. Single-span beams under the influence of a uniformly distributed load are considered. To determine the stress-strain state, the Ritz-Timoshenko variational method and the Lira software package were used. In the first case, the calculation was carried out in the Excel environment, while trigonometric functions were taken as approximating functions. It is shown that satisfactory results can be obtained with 6 terms of the series approximating the required function. Beams with different relative lengths are considered: short, medium and long. The influence of the degree of inhomogeneity of the base on deflections and bending moments is shown. It was found that in short beams with an increase in the degree of inhomogeneity of the base, the bending moments significantly increase. For long beams, the deflection values increase significantly. Calculations in the Lira software package, taking into account the symmetry of the problem, were performed for a half of the beam with a breakdown of the region into 20 elements. Within each element, the value of the bed coefficient was assumed constant. The results obtained in two ways are in complete agreement.
Influence of Inhomogeneity of the Foundation on the Stress-Strain State of a Free-Lying Beam
https://orcid.org/http://orcid.org/0000-0002-7191-1237
https://orcid.org/http://orcid.org/0000-0002-1032-5373
https://orcid.org/http://orcid.org/0000-0002-0998-4726
https://orcid.org/http://orcid.org/0000-0002-0251-9258
The stress-strain state of beams freely lying on an inhomogeneous elastic Winkler foundation is investigated. It is accepted that the value of the base bed coefficient has a symmetrical character of change relative to the middle of the beam, and within its limits is described by a quadratic law. Single-span beams under the influence of a uniformly distributed load are considered. To determine the stress-strain state, the Ritz-Timoshenko variational method and the Lira software package were used. In the first case, the calculation was carried out in the Excel environment, while trigonometric functions were taken as approximating functions. It is shown that satisfactory results can be obtained with 6 terms of the series approximating the required function. Beams with different relative lengths are considered: short, medium and long. The influence of the degree of inhomogeneity of the base on deflections and bending moments is shown. It was found that in short beams with an increase in the degree of inhomogeneity of the base, the bending moments significantly increase. For long beams, the deflection values increase significantly. Calculations in the Lira software package, taking into account the symmetry of the problem, were performed for a half of the beam with a breakdown of the region into 20 elements. Within each element, the value of the bed coefficient was assumed constant. The results obtained in two ways are in complete agreement.
Influence of Inhomogeneity of the Foundation on the Stress-Strain State of a Free-Lying Beam
https://orcid.org/http://orcid.org/0000-0002-7191-1237
https://orcid.org/http://orcid.org/0000-0002-1032-5373
https://orcid.org/http://orcid.org/0000-0002-0998-4726
https://orcid.org/http://orcid.org/0000-0002-0251-9258
The stress-strain state of beams freely lying on an inhomogeneous elastic Winkler foundation is investigated. It is accepted that the value of the base bed coefficient has a symmetrical character of change relative to the middle of the beam, and within its limits is described by a quadratic law. Single-span beams under the influence of a uniformly distributed load are considered. To determine the stress-strain state, the Ritz-Timoshenko variational method and the Lira software package were used. In the first case, the calculation was carried out in the Excel environment, while trigonometric functions were taken as approximating functions. It is shown that satisfactory results can be obtained with 6 terms of the series approximating the required function. Beams with different relative lengths are considered: short, medium and long. The influence of the degree of inhomogeneity of the base on deflections and bending moments is shown. It was found that in short beams with an increase in the degree of inhomogeneity of the base, the bending moments significantly increase. For long beams, the deflection values increase significantly. Calculations in the Lira software package, taking into account the symmetry of the problem, were performed for a half of the beam with a breakdown of the region into 20 elements. Within each element, the value of the bed coefficient was assumed constant. The results obtained in two ways are in complete agreement.
Influence of Inhomogeneity of the Foundation on the Stress-Strain State of a Free-Lying Beam
Lecture Notes in Civil Engineering
Klyuev, Sergey Vasil'yevich (editor) / Klyuev, Alexander Vasil'yevich (editor) / Vatin, Nikolay Ivanovich (editor) / Leontiev, A. N. (author) / Gorbunova, T. N. (author) / Balandina, K. V. (author) / Sitnikova, A. A. (author)
International Scientific Conference on Innovations and Technologies in Construction ; 2021 ; Belgorod, Russia
2021-03-29
8 pages
Article/Chapter (Book)
Electronic Resource
English
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